302 ELEMENTS OF SCIENCE 



we say " Some B is not A " we exclude some B from 

 the entire class of A, and so A is distributed. 



Various ingenious plans have been devised whereby 

 syllogisms of the second, third, and fourth figures qan 

 be converted into syllogisms of the first figure. This 

 process reposes upon those rules for the conversion of 

 propositions which have been hereinbefore given (pp. 293 

 and 294). But for an account of such devices the reader 

 is referred to special treatises on logic. 



In the second figure, the valid moods are : AEE, AGO, 

 EAE, and EIO. In this figure there must be a negative 

 premiss, and therefore a negative conclusion. Thus : 



All apes are mammals. 



But no gill-bearing creatures are mammals. 



Therefore no gill-bearing creatures are apes. 



If the second premiss were affirmative as well as the 

 first, the middle term would not be distributed, as, e.g., 

 with such premisses as " All apes are mammals," and 

 " Hair-bearing creatures are mammals," we can conclude 

 nothing because the middle term " mammals " is distri- 

 buted in neither case. For all that appears, there might 

 be (as, in fact, there are) mammals which are neither 

 " apes " nor " hair-bearing creatures." 



In this figure also the major premiss must not be 

 particular, as otherwise there would be a term distri- 

 buted in the conclusion which was not distributed in the 

 premiss, and this is against Rule 4 (p. 296). 



The third figure has the following valid moods : AAI, 

 All, EAO, EIO, IAI, OAO. Here there must be no 

 negative minor, but there must be a particular conclu- 

 sion. Thus : 



All mammals have warm blood. 



But all mammals are air-breathers. 



Therefore some air-breathers have warm blood. 



